Okay, I have this resolved. For anyone in a similar situation, you're not going to like it, but it works.
Step #1: Demand a refund from the iTunes Store for your $130 in-app purchase. Instructions on doing that can be found here: http://www.imore.com/how-to-get-refund-itunes-app-store
Be sure to explain to them that the subscription is supposed to work on any device using the same subscription. Also point them to the refund policy at nhl.com, which states that if you had bought it from their website instead of through the app you would have had 5 days to cancel and ask for a refund. Point out that you're within that window (or, if you're not, neglect to mention that detail and see what happens. I was within the window).
Step #2: Wait until they email you stating that you're getting a refund (took a little over 24 hours for me). Smile briefly, then remember you still can't watch the Blackhawks crush the other teams on their road to their next Stanley Cup.
Step #3: Swallow your pride and buy the subscription through the NHL website. Curse a few times if that helps.
Step #4: Delete your NHL app from your phone, then reinstall it. Do the same for any other IOS device you have.
Step #5: Reinstall the app. This time, instead of restoring purchases (which have been voided by your friendly neighborhood apple support person), sign in using your NHL credentials.
Step #6: Watch the games. Enjoy!
Step #7: Wait patiently for the refund they promised would arrive in 10 business days. Remember, it's apple and they promised. It'll happen.
I hope that's helpful to someone. I have learned my lesson -- I will never again purchase NHL packages, or any other sports package, through the app store. It's not their fault, but it's just too ****** hard for the developers to work across platforms, apparently.